毛囊间距反应扩散模型的时空模式和多重分岔

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-01-01 DOI:10.3934/era.2023099

Zhili Zhang, A. Wan, Hongyan Lin

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引用次数: 0

摘要

本文考虑了模拟毛囊间距的双分量耦合扩散系统的动力学行为。对于相应的微分方程，我们不仅考虑了唯一正平衡解的稳定性和不稳定性，而且证明了不稳定Hopf分岔周期解的存在性。对于反应扩散方程，我们主要关注正平衡解的图灵不稳定性，以及Hopf分岔和稳态分岔。结果表明，在一定条件下，反应扩散系统不仅具有Hopf分岔周期解(既有空间齐次的，也有非齐次的，均不稳定的)，而且具有非常正分岔平衡解。这可以让我们更清楚地了解这个特定系统的时空模式的机制。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Spatiotemporal patterns and multiple bifurcations of a reaction- diffusion model for hair follicle spacing

In this paper, the dynamical behaviors of a 2-component coupled diffusive system modeling hair follicle spacing is considered. For the corresponding ODEs, we not only consider the stability and instability of the unique positive equilibrium solutions, but also show the existence of unstable Hopf bifurcating periodic solutions. For the reaction-diffusion equations, we are mainly interested in the Turing instability of the positive equilibrium solution, as well as Hopf bifurcations and steady-state bifurcations. Our results showed that, under certain conditions, the reaction-diffusion system not only has Hopf bifurcating periodic solutions (both spatially homogeneous and non-homogeneous, all unstable), but it also has non-constant positive bifurcating equilibrium solutions. This allows for a clearer understanding of the mechanism for the spatiotemporal patterns of this particular system.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.